probability question
- Thread starter marley
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Probability of getting a blackjack: pBJ = 2*1/13*4/13 = 8/169
Probability of getting a blackjack of specific suit: pSBJ = pBJ / 16 = 1/338
How many hands you need, depends on the certainty you want to achieve your goal. Say you want to know the number of hands, that for a chance of C=95% you get all 4 suited blackjacks.
You need the number of hands N such that pH(N) * pS(N-1) * pC(N-3) * pD(N-4) = C, where pH(N) is the probability of getting at least 1 suited hearts blackjack within N hands, pS(N-1) is the probability of getting at least 1 suited Spades blackjack in N-1 hands... pC for clubs, pD for diamonds.
For a specific suit X:
pX(N) = 1 - (1-pSBJ)^N.
I'm sure you are not interested in the exact number, hence we neglect the "N-1", "N-2", "N-3" and set it to simple N.
Then P = (1 - 337/338^N)^4 = 0.95 gives N=1472.5
Probability of getting a blackjack of specific suit: pSBJ = pBJ / 16 = 1/338
How many hands you need, depends on the certainty you want to achieve your goal. Say you want to know the number of hands, that for a chance of C=95% you get all 4 suited blackjacks.
You need the number of hands N such that pH(N) * pS(N-1) * pC(N-3) * pD(N-4) = C, where pH(N) is the probability of getting at least 1 suited hearts blackjack within N hands, pS(N-1) is the probability of getting at least 1 suited Spades blackjack in N-1 hands... pC for clubs, pD for diamonds.
For a specific suit X:
pX(N) = 1 - (1-pSBJ)^N.
I'm sure you are not interested in the exact number, hence we neglect the "N-1", "N-2", "N-3" and set it to simple N.
Then P = (1 - 337/338^N)^4 = 0.95 gives N=1472.5
Sonny
Well-Known Member
I like your number better. Here's why:Zero said:
http://www.blackjackinfo.com/bb/showthread.php?p=48844
-Sonny-
Your 32/663 is correct for Single Deck. For infinite Deck it is 8/169. Since there is no number of decks stated in the original question, I like to use my personal choice of determing a deck number (as you did with single deck). Since infinite deck is a lot simpler (no card removal effects), this choice is a well accepted one.Zero said:
As it has already been pointed out, for probability of a specific suited BJ (not any suited BJ) you need to divide by 16 (not 4).
Cardcounter
Well-Known Member
The odds of getting a suited blackjack are 1 in 84. The odds of the dealer having an ace up when you have a blackjack in a single deck game is 1 in 16. Odds of getting a suited blackjack with an ace up in a one deck game is
1 in 1,344 off the top of the deck. If the count goes up the odds get better. If the count goes down the odds get worse.
1 in 1,344 off the top of the deck. If the count goes up the odds get better. If the count goes down the odds get worse.
In a single deck game, the dealer will have an ace up and you will get a suited BJ exactly once every 1371.25 hands.
13 * ((51/3 x 50/4) + (51/12 x 50/1)).
The chance of you getting a suited BJ in a different suit than the first one is 1 in 1841.667.
13 * (((51/3 x 50/4) + (51/12 x 50/1) + (3*(51/2 x 50/4) + (51/8 x 50/1)) /4)
The chance of the dealer having an ace up and you getting a suited BJ in one of the other two suits is 1 in 2762.5.
13 * ((((2 * ((51/2 x 50/4) + (51/8 x 50/1))) + (2 * ((51/1 x 50/4) + (51/4 x 50/1))) /4)
The chance of the dealer having an ace up and you getting a suited BJ in the FINAL suit is 1 in 5525.
13 / .75 * ((51/1 x 50/4) + (51/4 x 50/1))
Therefore; the chance of getting a suited BJ in all four suits when the dealer has an ace up is 1 in (1371.25 + 1841.667 + 2762.5 + 5525); or 1 in 11,500.417. In other words; if you play 8 hours a day 5 days a week,you ought to be able to "bat the cycle" about once a year.
13 * ((51/3 x 50/4) + (51/12 x 50/1)).
The chance of you getting a suited BJ in a different suit than the first one is 1 in 1841.667.
13 * (((51/3 x 50/4) + (51/12 x 50/1) + (3*(51/2 x 50/4) + (51/8 x 50/1)) /4)
The chance of the dealer having an ace up and you getting a suited BJ in one of the other two suits is 1 in 2762.5.
13 * ((((2 * ((51/2 x 50/4) + (51/8 x 50/1))) + (2 * ((51/1 x 50/4) + (51/4 x 50/1))) /4)
The chance of the dealer having an ace up and you getting a suited BJ in the FINAL suit is 1 in 5525.
13 / .75 * ((51/1 x 50/4) + (51/4 x 50/1))
Therefore; the chance of getting a suited BJ in all four suits when the dealer has an ace up is 1 in (1371.25 + 1841.667 + 2762.5 + 5525); or 1 in 11,500.417. In other words; if you play 8 hours a day 5 days a week,you ought to be able to "bat the cycle" about once a year.